Multi-Derivative Runge-Kutta Flux Reconstruction for hyperbolic conservation laws
arxiv(2024)
摘要
We extend the fourth order, two stage Multi-Derivative Runge Kutta (MDRK)
scheme of Li and Du to the Flux Reconstruction (FR) framework by writing both
of the stages in terms of a time averaged flux and then use the approximate
Lax-Wendroff procedure. Numerical flux is computed in each stage using D2
dissipation and EA flux, enhancing Fourier CFL stability and accuracy
respectively. A subcell based blending limiter is developed for the MDRK
scheme, which ensures that the limited scheme is provably admissibility
preserving. Along with being admissibility preserving, the blending scheme is
constructed to minimize dissipation errors by using Gauss-Legendre solution
points and performing MUSCL-Hancock reconstruction on subcells. The accuracy
enhancement of the blending scheme is numerically verified on compressible
Euler's equations, with test cases involving shocks and small-scale structures.
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